help-28

[wooden knoll]

you know this is your first

vertical asymptote

which is a start

[torn jolt]

I tried doing something similar but also the graph has to be put in a system

Let me show you

[wooden knoll]

ok

[torn jolt]

If I move one thing everything moves

[wooden knoll]

i see

alrighty

so the vertical asymptotes

are going to be pi units apart

right?

on a tan graph

so have your first asymptote at -pi/8

[torn jolt]

Yess I got that

[wooden knoll]

alright now for the streth

we see the coeffiiceint

is 9/2

[torn jolt]

Correct

[wooden knoll]

so where tan(x+5pi/8) = 1

tahts where 9/2tan(x+5pi/8) = 9/2

where does tan(x) = 1?

do you know?

[torn jolt]

I got confused

[wooden knoll]

my bad

[torn jolt]

It’s okay I’m just having a hard time understanding this 😭

[wooden knoll]

,,\tan\left(x+\frac{5\pi}{8}\right)

[glossy valve]

epiphonically

[wooden knoll]

focus on this part

Lets say this part = 1

,,\tan\left(x+\frac{5\pi}{8}\right)=1

[glossy valve]

epiphonically

[wooden knoll]

that would mean

,,\frac{9}{2}\tan\left(x+\frac{5\pi}{8}\right)

[glossy valve]

epiphonically

[wooden knoll]

would be?

[torn jolt]

1?-1?

[wooden knoll]

it would be 9/2

,,\tan\left(x+\frac{5\pi}{8}\right)

[glossy valve]

epiphonically

[wooden knoll]

the x value that makes this one

,,\frac{9}{2}\tan\left(x+\frac{5\pi}{8}\right)

[glossy valve]

epiphonically

[wooden knoll]

would make this 9/2

right?

[torn jolt]

Oh that makes sense

[wooden knoll]

so if we find that x value

we just move the slider at that place

to 9/2

the hard question is

,,\tan\left(x+\frac{5\pi}{8}\right)

[glossy valve]

epiphonically

[wooden knoll]

what x value makes this one

you know tan(pi/4) = 1

right?

[torn jolt]

Yes

[wooden knoll]

so

,,x+\frac{5\pi}{8}=\frac{\pi}{4}

[glossy valve]

epiphonically

[wooden knoll]

and thats our x value

where were gonna slide

the slider

up to 9/2

[torn jolt]

If I were to solve for x here that’ll be -3pi/8

[wooden knoll]

correct

are u allowed to

slidey

there?

[torn jolt]

Yeah

[wooden knoll]

show me what u have on ur pc

rn

[torn jolt]

Should I put the purple dot on top of that

Or the asymptote

[wooden knoll]

move the puprple dot at -3pi/8 up to 9/2

[torn jolt]

Did I do it wrong

[wooden knoll]

youre vertical asymptotes arei n the wrong spot

[nocturne pilot]

You just have to roughly show the graph?

And point the assymptotes I'm guessing?

[wooden knoll]

she has to move dots on her pc

[torn jolt]

Yeah if I move the purple dots I move everything in the graph

[nocturne pilot]

Did u try graphical tranforms?

[torn jolt]

Yeah

[nocturne pilot]

Did that not solve it?

[torn jolt]

[wooden knoll]

easy fix

dw

just move it

to -pi/8

remember

?

[torn jolt]

Okie the question is in this case where will -pi/8 be located

I’m sorry I’m stressing

[wooden knoll]

it should be an eighth of the way from pi

on the left side

to pi

sorry

not from

an eighth of the way to pi

[torn jolt]

I’ve tried to put it in the calculator too

[wooden knoll]

yea there

[torn jolt]

I don’t know how to put it in the systemmm 😭😭

It’s so frustrating

[wooden knoll]

move it to where i drew the red line

does it let u?

[torn jolt]

Yes

But what about the purple dot

I’ve tried to locate the blue dot at 4.5

Also another question. Will my purple dot be on top of the x-axis or at -1

[wooden knoll]

-1

but i reccomend

doing that last

cause its gonna make the blue dot harder to place

[torn jolt]

Okie so here is the asymptotes

I GOT IT

Omg I got it right

[wooden knoll]

ok

nice

[torn jolt]

I love you and I don’t even know you

Thank you so much

[wooden knoll]

np

[torn jolt]

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[tepid raven]

<@&286206848099549185>

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@tepid raven Has your question been resolved?

[tepid raven]

@outer ocean What??

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[tepid raven]

<@&286206848099549185>

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@tepid raven Has your question been resolved?

[daring citrus]

isnt 2a) just
40000×(1+0.08×2.5) ?

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@tepid raven Has your question been resolved?

[tepid raven]

@daring citrus Yes, that’s what I thought too. But you mean ^2.5 ? As an exponent right?

That’s what I did

[daring citrus]

depends if its simple interest or compound

[tepid raven]

I was taught to use this formula on these kind of problems: f = p * (1 + y)^n

[daring citrus]

yeh then use that one

[tepid raven]

That’s compound right?

[daring citrus]

yep

[tepid raven]

Cool. Are you good with these kind of problems in finance?

I could use some help sometimes lately if you’re open to it.

[daring citrus]

i cant guarantee
i can only tell after seeing the question

[tepid raven]

Okay. Yeah that’s all I really want is to be able to check my work with someone who understands finance for the most part.

Would you mind if I add you or pm you if anything comes up?

[daring citrus]

i think the best way to do it would be just using the server itself
but if in case noone answers for too long then you can dm me :)

[tepid raven]

Ok no problem, thank you

[tepid raven]

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[tepid raven]

.reopen

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✅

[tepid raven]

@daring citrus What would you do for these problems?

[short crest]

is this only for alpha kappa?

or can i answer

[daring citrus]

you can

[short crest]

nvm im playing rn

[daring citrus]

lmao

[tepid raven]

Sure anyone can answer @short crest Thank you

@ my name when you figure the problems out @short crest

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[gritty rose]

.close

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[shrewd tusk]

Hey. I'm trying to identify a piece of mathematics software that does visualisations. Its logo is the Lambda symbol (λ) on a blue and red background. Does anyone have an idea what it could be?

[fast peak]

racket?

[wild sleet]

dr racket yeah

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[shrewd tusk]

That's it, thanks!

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[little river]

(b) Let I ⊆ R be an ideal and let π : R → R/I, a → [a]_I. Show that

π : R^{n,n} → (R/I)^{n,n}, [a{ij}] → [(a_{ij})]

is a surjective ring homomorphism of the rings R^{n,n} and (R/I)^{n,n}.

[stiff musk]

R^{n,n} denotes the set of n x n matrices whose entries are values of R?

[little river]

I think so, yes

<@&286206848099549185>

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[little river]

hello?

.closed

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[copper condor]

hey so im workig on a project right now trying to relate quadratic inequalities to real life physics and i need an opinon if thats alll right

[atomic blade]

so what if a cannon ball was shot at an angle and it had to clear over a wall that is 37 feet tall to destroy the castle of Sir Urmomisphat's Kingdom?

that is one example

[copper condor]

so i have to sovle to find the angle

?

because the whole point of the project is to relate to real life

why did u delete?

[atomic blade]

Delete what

[copper condor]

what u said

[atomic blade]

I didn't delete anything

I just edited it

[copper condor]

something about time

i was reading then it disapperaed

[atomic blade]

I never said anything about time

Prob someone else did

[copper condor]

WAIT HUH

it was likfe time it takes to go over the wall

[atomic blade]

I never said that

[copper condor]

https://tenor.com/view/awkward-stare-dog-stare-dog-brows-funny-gif-12521793

[atomic blade]

I think you're hallucinating

[copper condor]

do my eyes deciece me

[atomic blade]

Yeah they do lol

I mean it's a physics problem

You can use your fancy physics equations and all that to do it

I haven't taken physics yet so I don't know them but I just provided an example

[copper condor]

im not trynna do all tha tlma

i just need to relate quadratic ineqaliteis an physics into a rael ife scnario

[atomic blade]

Oh yeah then you can use that

Don't worry about angles

"A cannon shoots a cannonball represented by quadratic f. 50 meters away from the cannon, there is a wall that is 37 meters tall. Will the cannon ball clear the wall?"

[copper condor]

so how would i have to solve something like atht

cause im still a little confused

[atomic blade]

I mean that is just an example

You don't have to solve it

That is one way you can relate it

By giving a real world scenario

[copper condor]

well the whole point is that i have to make a step by step process on solving the problem by giving a presentaion

[atomic blade]

Oh that's not too bad

[copper condor]

yea im just dumb lmao

[atomic blade]

Well you need to find some realistic equation for f

[copper condor]

would finding the distance of a ball dropping in the time period of 3 seconds work as a rea life scenario

with the equation

d=ViT + 1/2at

[atomic blade]

To be honest I have not taken physics so I don't know

All you do is find the equation for the trajectory and use an inequality to express the domain at which it clears the height of the wall, w

So that f(x) > w

[copper condor]

https://tenor.com/view/thinking-hard-carlo-boszhard-the-masked-singer-wait-im-thinking-im-trying-to-think-gif-19725133

im trying to think and proccess this

cause im not to keen with math or physics lol

could we get someone who knows physics in here aswell for there physics opinion

[atomic blade]

Yeah you could

Hopefully helpers have taken it

[copper condor]

so should i ping them

<@&286206848099549185>

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@copper condor Has your question been resolved?

[stray abyss]

yes this would work

rectilinear motion would be better to work with

unless u want to make it fancy

[copper condor]

its for math 3

and its only a 4 min presentaion

but what is the quadratic inequalites

in the problem

[stray abyss]

should be fine then i believe

so it's not exactly distance travelled in that time

u could set up a range for the height u want to reach / distance to cover

and work out the range of initial velocity / the time of flight

[copper condor]

so waht would the inequality be then

so i cant stick to the basic just trying to find the basic distance

using d=ViT + 1/2at

[stray abyss]

1/2at^2

[copper condor]

d=1/2at^2

?

[stray abyss]

so what do u want to do? drop a ball from a height or throw a ball up?

[copper condor]

drop from height

[stray abyss]

ok

[copper condor]

do u minf if i add u too a clall

with my partent

cauuse i gotta mulkti task with him

[stray abyss]

hmm not really

like i could work on text

[copper condor]

yea yea thats no prob i just thoguth it would be easier

but its fine g on

[stray abyss]

but i have some work coming up so can't really help much / i'll leave midway

[copper condor]

thats fine

could u try as much as u can>

?

tahst fine

[stray abyss]

honestly there's nothing much really

[copper condor]

so basically can i talk about a baseball i want to drop and i want to find disatance covered ovet the course of 5 seconds and accelataion is 9.8 would the whoel thign look like

d = 1/2 (9.8) (5) ^2

[stray abyss]

but that would be an exact case

u want an inequality

[copper condor]

so how woiuld i make it into an inequality

[stray abyss]

so one idea could be

u have some sort of a detector which detects a ball in front of it

and it's placed over a length of say 2 m

and u drop a ball from above

so over what time interval will the detector detect the ball?

something like that

and the ball is dropped from say 10m above

i hope u get the situation

[copper condor]

https://tenor.com/view/math-zack-galifianakis-thinking-calculating-gif-5120792

soooooooooooooooo how would i solve that in a

equation

[stray abyss]

so u have say the starting point of the detector and the end point

then starting<distance<end

[copper condor]

https://tenor.com/view/crying-black-guy-meme-sad-gif-11746329

I CANT COMPREHEND MAN

im about to fail this thing

[stray abyss]

rough sketch

so u need to find the time interval in which the ball lies in the blue region

which is the detector

[copper condor]

and how would i do that excatly

https://tenor.com/view/hmmm-thinking-batman-gif-14744673

[stray abyss]

not sure if i can explain further

[copper condor]

why not?

[stray abyss]

.

[copper condor]

so theres no tecnical equation

[stray abyss]

?

what does that mean

[copper condor]

like theres no equation to solve for the interval of time
cause im pretty sure this (then starting<distance<end) isnt an equation i can use to solve

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[lucid thorn]

I need the answer for f(-10). Thanks!

[atomic blade]

Which partition contains -10 in its domain

[lucid thorn]

Not sure what you mean by that.

[atomic blade]

You have three partitions

t^2-5t

t+19

t^3/(t+9)

They're restricted by certain domain restrictions

So which restriction contains -10

Look at the first one. It's $t\leq -10$. What does that mean

[glossy valve]

Umbraleviathan

[lucid thorn]

Less than or equal to.

[atomic blade]

Yeah

The "or equal to" part indicates that it includes -10

So just plug in -10 into the first partition

[lucid thorn]

Ok, thanks.

Sorry for being dumb 💀

[atomic blade]

Np lol

[lucid thorn]

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[dawn kettle]

Hi, good morning, afternoon or night

[dawn kettle]

So, I have to do this exercise, in which [(x^4 + 7x^2 + 7)^1/2] f'(x) = (2x^3 + 7x)f(x)

And f(0) equals e^2[(7)^1/2]

I think I'm almost done with it

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[tiny mango]

So finding c is the next step right?

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[torn jolt]

I'm struggling to follow an equivalency given by a practice assignment. This is the first equivalency

https://i.imgur.com/IDY75HO.png

It then goes to say "Obviously $E$ and $F$ are independent exactly when $$(n+1)/n = 2^{n-1}/(2^{n-1}-1).$$" So far so good, I follow. The equation needs to be 1 so the independency works.

However, it loses me when it says "Especially, $n=2^{n-1} - 1$ needs to hold". But... I'm not sure how that follows. I can't figure out a way to alter the formula algebraically to that equivalency, and I'm unaware of any rule that would allow me that conclusion. Admittedly I still struggle with Maths sometimes, so any help would be appreciated.

[glossy valve]

Dye

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[torn jolt]

<@&286206848099549185>

[torn jolt]

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[limpid ore]

Below is the graph of the function: f(x)=0.25x^3+6x^2 with 0<x<30. Also drawn is the line y=-27x. Using differentiation, calculate the x-coordinate of the vertex of the graph of f on the interval [0.30].

.close

<@&268886789983436800> can you delete this

[deft juniper]

it is closed

it will be removed soon

[limpid ore]

O ok tnx

Can you help at the other

[deft juniper]

yes

[slender onyx]

yeah deleting the question closes the channel

[limpid ore]

Help 30

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[zenith mantle]

What is all of this and how?

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[zenith mantle]

<@&286206848099549185>

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[zenith mantle]

.close

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[analog cosmos]

1 sec

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[torn jolt]

Looks fine to me

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[sonic sparrow]

if
a+b+c= ax +by +cz
then
x=y=z?

[mighty widget]

try plugging numbers

[sonic sparrow]

i mean if x=y=z, then theyre all equal to one

[sonic sparrow]

m actually tryna prove something else

[sonic sparrow]

so i need to know if this holds true

[nova basin]

No it doesn't. For this to be true, you would need to be at least in a 3D vector space (R is 1D, the set of all real multiples of 1), and even then it's not guaranteed.

[sonic sparrow]

fk :)

thx anyways

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[deft juniper]

For b) I understand it's basically asking P(L>20|L>16)

[deft juniper]

Normally to calculate this I would use P(AnB)/P(A) = P(B|A)

how would I calculate P(AnB) in this case

or is P(AnB) = P(B) becasuse L>20 intersects L>16 for L>20

idk if that makes sense or not

<@&286206848099549185>

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[cinder kayak]

@deft juniper Let me check it. Pls reopen the chat

[cinder kayak]

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[cinder kayak]

(I am answering the question of @deft juniper , which is closed due to inactivity)
Let P(L>20 and L>16) = P(L>20)

[glossy valve]

kelvinchan9786

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[torn jolt]

I know this is physics, but it has mainly math. What is the partial derivative of the equation on the bottom with respect to x?

[queen pond]

bottom right ? huh?

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[trim swift]

hi i just want to know if a will be equal to both of the equations since they are parallel

😕

[light sonnet]

Yes the slopes of parallel lines are the same

[trim swift]

ok

thanks

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[spare nacelle]

hello if k = 0, would this result in just (a_n, b_n] or {}?

[rare dock]

I'd guess it's a typo and it was supposed to say n=0 or k>=1 haha

I don't think that notation makes any sense when k=0

[spare nacelle]

that what i wrote is technically this, right?

Like does the thing get called once or doesnt even start

[fast peak]

the empty union is typically defined to be the empty set

[rare dock]

I guess I'd read it as $]a_1,b_1]\cup]a_0,b_0]$ when $k=0$ if you wrote it like that but I'd still be wondering why it was written like that

[fast peak]

similar to how the empty sum is 0 or the empty product is 1

[glossy valve]

Spring

[spare nacelle]

Ok so that tells me that the empty set exists in R as a better proof

for k=0

denascite can u approve

[fast peak]

yes

[spare nacelle]

ty

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[late cypress]

is the answer right

500000

vertex 5/6

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[late cypress]

<@&286206848099549185>

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@late cypress Has your question been resolved?

[cinder kayak]

Could you show whole question?

[late cypress]

sory it's kinda blurry

@cinder kayak

[cinder kayak]

It's ok. Let me read it...

@late cypress Yes, same with my work

[late cypress]

let's say the equation is y=(x+20)(20000-650x)

would the max income be 400000

@cinder kayak

[cinder kayak]

should be y=(x+25)(20000-650x)

[late cypress]

for the income to be 400000

[cinder kayak]

y=(x+25)(20000-750x)

[late cypress]

ya but let's say we change the equation

to y=(x+20)(20000-650x)

since y=(x+25)(20000-750x) the max income is 500000 right?

[cinder kayak]

Hmmm...how do you get max. revenue of $400000?

@late cypress

if y=(x+20)(20000-650x)

[late cypress]

418846

mb

@cinder kayak

i just resubbed in the equation

[cinder kayak]

It is correct now

[late cypress]

i think so

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[chrome idol]

Is D3 isormorphic to S3?

[chrome idol]

It is right? Since D3 is a subgroup of S3?

wait nvm, I dont think that proofs its isomorphic

From an excercise in the previous chapter, I know every element in D3 corresponds to an element in S3

I think this is a proof?

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[opaque helm]

Wait nvm

[fathom saddle]

Yeah you basically have to construct the function from one to the other

Or, show that this is the only group of order 6 with some property

[opaque helm]

I think this is a proof too

Like, that's basically constructing the isomorphism of groups between the two groups

Btw you could have created such isomorphism with only 2 elements, the generators

[chrome idol]

hmm ok

make sense

thanks

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[chrome idol]

.reopen

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✅

[chrome idol]

I found this theorem here

Does this help at all for the question?

Im not sure how the group of permutations of S3 is

[spice orchid]

How many elements does D3 have?

[chrome idol]

6

[spice orchid]

So D3 is isomorphic to a subgroup of S3, and it has 6 elements. Do you see how that implies it is isomorphic to S3?

[spice orchid]

This picture also gives you the explicit isomorphism

[chrome idol]

is this from the result from Cayleys Theorem?

[spice orchid]

Don't even need Cayleys theorem here, it's a subgroup of size 6, of a group of size 6, so it must be (isomorphic to) the whole group

[chrome idol]

could you state that more explicitly? Im having some trouble following the logic

[spice orchid]

"If a box only holds 6 things, and I put 6 things in it, have I filled the box up?"

[chrome idol]

yeah

Ok, so then this shows there exist some isomorphism, right

[spice orchid]

Yes, D3 is iso to some subgroup of S3, but since D3 and S3 both have 6 elements, the only subgroup it can be iso to is the subgroup of S3 with 6 elements, which is the whole of S3

[chrome idol]

ok, that makes sense

I think my problem is that, this feels very detached from the definition of isomorphism , specifically the homomorphism part

[spice orchid]

Sorry the answer to this should have been yes, I am using cayleys theorem. Cayleys theorem is powerful as we can show things are isomorphic without having to explicitly construct the isomorphism

As I said, the picture you sent is an explicit construction of the isomorphism

[chrome idol]

So in this case, what is "G"?

D3 or S3

It should be D3 right? Since S3 is the symmetric group, which is literally defined as the set of all permutations of D3

And for D4 and S4, they should obviously not be isomorphic, since they have different orders

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[gray nacelle]

can someone give me tips on how to approach this question using math induction?

[gray nacelle]

i think i know whats induction, but the process of proving the steps is really hard for me

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[gray nacelle]

<@&286206848099549185>

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@gray nacelle Has your question been resolved?

[chrome idol]

What have u got so far

Have you verified the base cases?

What’s the induction hypothesis

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[torn jolt]

Need some advice on logic
I want to make a formula so that it is acepted by the natural numbers but not by the amount of the whole numbers

Currently got this :
There exist an x(exist an y( exist an z( (x*y=z )and x<y and y<z)))
Would that be correct?

F.ex 12=2would be acepted but
-32=-6 would not or?

[dreamy mason]

Your assertion doesn't make sense if you don't precise the sets in which you choose your variables x,y and z.
For example, if x,y and z are complex number, then the "x<y and y<z" part won't make sense.

[torn jolt]

Natural numbers as in {1,2.....} and whole numbers as in {-1.....0.....}

So no complex numbers

Or am i misunderstanding you?

[dreamy mason]

I know right, what I mean is that we can't know what numbers are x,y and z if you don't precise it in your formula

[torn jolt]

Is it enough if i give a structure? Like N=(N,<,) Z=(Z,<,)?

Or must it be specifically in the formula

Sorry i am a little confused

[dreamy mason]

It is fine, actually you just need to add:

There exist a natural number x(exist a natural number y( exist anatural number z( (xy=z )and x<y and y<z)))

With these additional details, your formula would be defined for the cases where x,y and z are all natural numbers

So -3*2=-6 wouldn't be accepted because x and z are defined as natural numbers

[torn jolt]

Ok i think i got it thank you very much

[dreamy mason]

No problem, in terms of symbols, it would just mean to write ∃x∈N instead of ∃x

[torn jolt]

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[stable spear]

Guys, I have just started summer school in Calculus. I am already losing myself. What we did during the lesson did not completely cover what we were given as homework. We were not taught derivatives yet (thats our next unit). We are using the method of f(x+h)-f(x)/h
But I do not understand the questions fully... Can anyone please help?

[floral crystal]

Could I ask you a question? what do you think h mean here?

[stable spear]

Since we only did determining of the tangent slope with this method I have only started question 4

After some algebraic work I have got the answer to be m=2 but that is where I am stuck now.

[floral crystal]

in the equation

f(x+h)-f(x)/h

[stable spear]

is not h our difference between our x points?

[floral crystal]

correct

[stable spear]

What am I supposed to do here sir? Like I found out that m=2 but the answer sheet gives a different answer because of this part. What does this part mean?

I did m=lim ((h^2+2h+1)-3)-(-2) and all of that /h
h--->0

after some work I got m=lim h(h+2)/h so I cancelled the h
h---->0

Lastly, I have inserted the 0 from the h-------->0 and so I got m=0+2...... which is 2.

But they did this. What does this mean?

[floral crystal]

So I'm confused by what you wrote here. What substitution did you make

[floral crystal]

ok you shouldn't be doing substitution at the very beginning

as that leads to some obvious errors

solve it with the variables first

[stable spear]

We were only taught this method today, we never learned derivatives as that is our next unit. What would you do sir?

[floral crystal]

Ok give me a sec

the value of f(x+h)= x^2 -2hx +h^2 - 3

f(x+h) - f(x) = -2hx + h^2

Also the question you solved is the inverse of the problem it is 3- x^2 while you solved x^2-3

[stable spear]

Am I not allowed to flip the equation?

is not x^2-3 the same as 3-x^2?

[floral crystal]

no -1* (x^2-3 ) = -x^2 + 3 = 3 - x^2

They are not the same. which explains why the answer is the inverse of the actual answer

[stable spear]

I see sir. Give me one second sir. Just one moment.

what would we do here sir?

so I have (3-(h^2+2h+1))

This is where I have made a mistake I believe. That is why I tried doing the inverse I guess.

Now that I found -2 as you said before

I finally did the right one, and not the inverse. Could you please explain me this part of the question?

<@&286206848099549185>

[brisk obsidian]

Give me one moment to make a graph.

[stable spear]

Thank you for offering help guys. This means a lot.

[brisk obsidian]

https://www.geogebra.org/classic/ukrgbr6p

[stable spear]

thank you so much sir

[brisk obsidian]

As you make h smaller and smaller, you will notice that the slope approaches a particular value.

[stable spear]

yes

[brisk obsidian]

This is an application of the Mean Value Theorem and Limits.

[stable spear]

I see

I understand that part that a tangent line crosses one point but that the secant crosses two

P and Q favourably

so we have to mmove it as close to the tangent as possible

[brisk obsidian]

That is how a limit is used to determine the slope at a point, x_0, on a function, f(x).

[stable spear]

yes

[brisk obsidian]

To determine the slope of a line, you need two points which gives you a change in y over a change in x.

[stable spear]

what if we are given multiple points sir?

[brisk obsidian]

However, given a single point on a curve, you cannot directly determine its slope because it is a single pont.

[stable spear]

one short question in between, is this correct sir? Solutions are not given for the 5th question here.

[brisk obsidian]

So we use limits to estimate a slope at a single point by making the observation that as the distance between x_0 and x_h gets smaller and smaller, it does a great job of approximiting the slope at x_0.

[stable spear]

yes

we were taught this m=lim
h----->0

method

[brisk obsidian]

Yes.

[stable spear]

to determine the exact

lim

and not just like aprox, which was did with another method which my class did not cover

it was this one with 0.0001 something

but it is irrelevant anyways since the other one is much more accurate right

so yes I did understand that part. I just did not understand the question itself , like I can do the method

[brisk obsidian]

So the question is asking you to use the given values of x_0 and approximate the slope at that point by finding the slope of secant lines whose points get closer and closer.

[stable spear]

like the 0.1, 0.01 etc?

Sorry that I am so stupid sir

but I just do not understand. I know how to find the lim with the method I just explained. I do not know what the question wants more from me, or how to get there

[brisk obsidian]

$(x_{0}, f(x_{0}))$ to $(x_{0}+x_{h}, f(x_{0}+x_{h}))$

[glossy valve]

Kookiemon

[brisk obsidian]

Using those points, you can find the slope.

As x_h gets smaller and smaller, you will find that the slope becomes an approximation of the slope at x_0.

[stable spear]

I understand the visualization

it perfectly makes sense, it is the algebra that now confuses me a little bit

like the x0 is our 0.001?

that is given in the question right

[brisk obsidian]

The question just wants you to approximate the slope at each given x_0.

Using the aforementioned method.

[stable spear]

so to approximate is not exact like what I did

I am sorry to bother you this much sir, would you please just show me an example?

[brisk obsidian]

No worries, I wouldn't be here if I wasn't interested in helping.

[stable spear]

Like I found the m= 1/2sqrt2

I found the solution to be this

this table I do not understand sir

Like my result is exact, therefore it is 0.35 smth if we turn it into a decimal

what does this table represent sir?

Does it represent the h getting smaller?

Because that does make sense, we want to be as close as possible, so we make it smaller right. But I just do not seem to completely get it...

Like the numbers inside

[brisk obsidian]

So the first column, x_p, would be x_O in my example.

And x_q would be the difference, h.

[stable spear]

oooh now I see

that is the problem, they do not say that in the question.

so the original is sqrt 2 so to speak

but how do we get 1.449? Isnt sqrt2 = 1.41

I found 4 mistakes so far in this homework sir... 😄 and the hw is given by waterloo!

exactly

thats what I did understand but 1.41 + 0.1 isnt 1.49 it is 1.51 right?

so therefore it did not maky any sense t ome

[brisk obsidian]

Well, actually ...

f(x_p) will still give sqrt( x_p + 2).

So actually, I'm mistaken.

Ok, let me take a step back because I was mistaken.

[stable spear]

No problem sir, thank you for your patience.

[brisk obsidian]

So the function f(x) = sqrt( x + 2).

x_p is the point whose slope you are trying to determine.

x_q is the point which is getting closer and closer to x_p which are used to determine a secant line with a slope.

[stable spear]

I see

but where does the 1.49 come from?

shouldnt it be 1.51?

[brisk obsidian]

Given x_p = 0, f(x_p) = sqrt( 0 +2) = sqrt(2).

$x_{p} = 0 \
f(0) = \sqrt{0+2} = \sqrt{2}$

[glossy valve]

Kookiemon

[brisk obsidian]

The 1.449 comes from

$x_{q} = 0.1 \
f(0.1) = \sqrt{0.1 + 2} = \sqrt{2.1} \approx 1.449$

[glossy valve]

Kookiemon

[stable spear]

Sir

you are the man

I am finally

understanding now

And so now that we have our

2 x values so to speak

we can finally use the formula m= y2-y1/x2-x1

right?

[brisk obsidian]

Yes, and that is given to you in the last column of the chart.

[stable spear]

I see

I finally understand

so to sum it up

our new value is basically just adding the 0.1 or 0.001 etc.

and finding the aprox value

of the rate of change which is m

which is not going to be as precise as using the method

m= lim
h---> 0

it is just there to highlight that right?

[brisk obsidian]

The limit will give you a precise answer because the limit assumes an infinitesimally small value for h.

This question is just showing you why it works.

[stable spear]

We are actually never really reaching that point

but at the same time we are, pretty weird when I think about it.

It is like walking towards a wall

but never reaching it

in a way.

[brisk obsidian]

Yeah, it is weird and quite a leap of logical faith. 🙂

[stable spear]

sir

since you are the math enthusiast here

let me give you one equation

do with it waht you want, you dont have to touch it

im just curious here you go:

ill give you two actually

All I know, is that they are impossible to solve using graph analytical technique

anyways, thank you for your help all the best sir!!!!

[brisk obsidian]

yw 🙂

[stable spear]

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[clever cargo]

This seems like a question for you to apply L'Hospital Rule

[nocturne creek]

No i have to do without that

[clever cargo]

......help

oki I'll leave that to other helpers then

[nocturne creek]

I think its n=2 but idk why it says n=4

[clever cargo]

So you tried using Maclaurin Expansions

[nocturne creek]

Yes

Oh shit

I forgot that there is an e^x

[clever cargo]

lol

yeah

happens

[nocturne creek]

No but

Rhat doesnt change the ans💀

Does it

[warped frigate]

Can someone help me solve for z

[nocturne creek]

Nah idk any geometry 😞

[warped frigate]

oof

[whole inlet]

is this 2d geometry?

[warped frigate]

yea

[whole inlet]

thx

[nocturne creek]

Are u here

[clever cargo]

yep

Wait

What

One question was already active

[nocturne creek]

If i write the e^x expansion i dont think it changes anything

[clever cargo]

Alright let us first check how it's even n = 4 or not

then we'll try to find a process which is not L'Hospital

[nocturne creek]

Okay i see

For n=2 the problem is it becomes 0

I can see for n=3 it is also 0

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@nocturne creek Has your question been resolved?

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@nocturne creek Has your question been resolved?

[nocturne creek]

i also need help with this

Okay actually

Would this be correct?

[nocturne creek]

okay ive got why for n=4, it is non zero

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